document.write( "Question 60613: The sum of two numbers is 33. Their difference is 9. What are the two numbers? This is how I solved am I right if not what did I do wrong?\r
\n" ); document.write( "\n" ); document.write( " x+9=33
\n" ); document.write( " y-9=33
\n" ); document.write( " 24+9=33
\n" ); document.write( " 42-9=33
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Algebra.Com's Answer #854295 by ikleyn(53874) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "The sum of two numbers is 33. Their difference is 9. What are the two numbers?
\n" ); document.write( "This is how I solved am I right if not what did I do wrong?
\n" ); document.write( "x+9=33
\n" ); document.write( "y-9=33
\n" ); document.write( "24+9=33
\n" ); document.write( "42-9=33
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\n" ); document.write( "\n" ); document.write( " The answer by @consc198, \"Yes this is correct \", is WRONG.\r
\n" ); document.write( "\n" ); document.write( " For a correct solution see what follows.\r
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document.write( "Let the numbers be x and y: x the greater, y the smaller.\r\n" );
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document.write( "From the problem, you have these two equations\r\n" );
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document.write( "    x + y = 33,\r\n" );
document.write( "    x - y =  9.\r\n" );
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document.write( "To find x, add the equations. You will get\r\n" );
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document.write( "    2x = 33 + 9,  or  2x = 42,  x = 42/2 = 21.\r\n" );
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document.write( "To find y, from the first equation subtract the second equation.  You will get\r\n" );
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document.write( "    y - (-y) = 33 - 9,  or  2y = 24,  y = 24/2 = 12.\r\n" );
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document.write( "ANSWER.  The numbers are 21 and 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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\n" ); document.write( "\n" ); document.write( "For this problem, and for many other similar problems, there is a shortcut,
\n" ); document.write( "which allows to get the answer MENTALLY and quickly:\r
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\n" ); document.write( "\n" ); document.write( "- - - one number is half-the-sum, while the other number is half-the difference of the given numbers.\r
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\n" ); document.write( "\n" ); document.write( "In our case, one number is $\"%2833%2B9%29%2F2\"$ = $\"42%2F2\"$ = 21; the other number is $\"%2833-9%29%2F2\"$ = $\"24%2F2\"$ = 12.\r
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